Analytic and asymptotic properties of non-symmetric Linnik's probability densities
| buir.advisor | Ostrovskii, Lossif V. | |
| dc.contributor.author | Erdoğan, M. Burak | |
| dc.date.accessioned | 2016-01-08T20:12:23Z | |
| dc.date.available | 2016-01-08T20:12:23Z | |
| dc.date.issued | 1995 | |
| dc.description | Ankara : Department of Mathematics and The Institute of Engineering and Science of Bilkent University, 1995. | en_US |
| dc.description | Thesis (Master's) -- Bilkent University, 1995. | en_US |
| dc.description | Includes bibliographical references leaves 44-45 | en_US |
| dc.description.abstract | We prove that the function 1 , a 6 (0 ,2 ), ^ e R, 1 + is a characteristic function of a probability distribution if and only if ( a , 0 e P D = {{a,e) : a € (0,2), \d\ < m in (f^ , x - ^ ) (mod 27t)}. This distribution is absolutely continuous, its density is denoted by p^(x). For 0 = 0 (mod 2tt), it is symmetric and was introduced by Linnik (1953). Under another restrictions on 0 it was introduced by Laha (1960), Pillai (1990), Pakes (1992). In the work, it is proved that p^{±x) is completely monotonic on (0, oo) and is unimodal on R for any (a,0) € PD. Monotonicity properties of p^(x) with respect to 9 are studied. Expansions of p^(x) both into asymptotic series as X —»· ±oo and into conditionally convergent series in terms of log |x|, \x\^ (^ = 0 ,1 ,2 ,...) are obtained. The last series are absolutely convergent for almost all but not for all values of (a, 0) € PD. The corresponding subsets of P D are described in terms of Liouville numbers. | en_US |
| dc.description.provenance | Made available in DSpace on 2016-01-08T20:12:23Z (GMT). No. of bitstreams: 1 1.pdf: 78510 bytes, checksum: d85492f20c2362aa2bcf4aad49380397 (MD5) | en |
| dc.description.statementofresponsibility | Erdoğan, M Burak | en_US |
| dc.format.extent | i, 45 leaves | en_US |
| dc.identifier.uri | http://hdl.handle.net/11693/17671 | |
| dc.language.iso | English | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Cauchy type integral | en_US |
| dc.subject | Characteristic function | en_US |
| dc.subject | Completely monotonicity | en_US |
| dc.subject | Liouville numbers | en_US |
| dc.subject | Plemelj-Sokhotskii formula | en_US |
| dc.subject | Unimodality | en_US |
| dc.subject.lcc | QA273.6 .E73 1995 | en_US |
| dc.subject.lcsh | Distribution (Probability theory). | en_US |
| dc.subject.lcsh | Functions, characteristic. | en_US |
| dc.title | Analytic and asymptotic properties of non-symmetric Linnik's probability densities | en_US |
| dc.type | Thesis | en_US |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Bilkent University | |
| thesis.degree.level | Master's | |
| thesis.degree.name | MS (Master of Science) |
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